Layer chicken, great northern beans, and corn in a slow cooker.
Mix chicken broth, condensed soup, chile peppers, and taco seasoning together in a bowl. Pour broth mixture over top.
Cover and cook on Low until chicken is no longer pink in the center and the juices run clear, 8 to 10 hours. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).
Transfer chicken to a cutting board. Shred with two forks or cut into bite-sized pieces. Return to the slow cooker.
Stir in sour cream and pepper Jack cheese; cover and cook on Low until cheese is melted, 3 to 5 minutes.
Notes
Recipe Tip
If you use cooked, chopped chicken in Step 2, you can cook it on Low for 3 to 4 hours.